An all-optical multidirectional mechano-sensor inspired by biologically mechano-sensitive hair sensilla

Mechano-sensitive hair-like sensilla (MSHS) have an ingenious and compact three-dimensional structure and have evolved widely in living organisms to perceive multidirectional mechanical signals. Nearly all MSHS are iontronic or electronic, including their biomimetic counterparts. Here, an all-optical mechano-sensor mimicking MSHS is prototyped and integrated based on a thin-walled glass microbubble as a flexible whispering-gallery-mode resonator. The minimalist integrated device has a good directionality of 32.31 dB in the radial plane of the micro-hair and can detect multidirectional displacements and forces as small as 70 nm and 0.9 μN, respectively. The device can also detect displacements and forces in the axial direction of the micro-hair as small as 2.29 nm and 3.65 μN, respectively, and perceive different vibrations. This mechano-sensor works well as a real-time, directional mechano-sensory whisker in a quadruped cat-type robot, showing its potential for innovative mechano-transduction, artificial perception, and robotics applications.

The above experimental results indicate that the strain effect on the microbubble is the main reason for the shift in the resonance wavelength.Under the same external force, the strain effect on the solid microsphere is much weaker than that on the hollow microbubble.
For the four microbubble-based mechano-sensors, the strain effect on the microbubble is not significant if the elastic modulus of the polymer matrix encapsulating the mechano-sensor is small, and the microbubble cannot deform if the elastic modulus of the polymer matrix encapsulating the mechano-sensor is too large.Therefore, the strain effect on the microbubble is strongest at an intermediate value of the elastic modulus.external force Fr is applied in the φ = 0° direction (Supplementary Fig. 3a), and the corresponding displacement is 2 μm.The stress field distribution in the equatorial crosssection of the mechano-sensor is shown in Supplementary Fig. 3b.The microbubble and fiber taper move in the φ = 0° direction, and the stress effect of the polymer matrix is negligible.

Supplementary
The radial strain dR/R and the strain-induced effective refractive index change dneff/neff in the equatorial cross-section of the microbubble are the averages of their field distribution integrals (Supplementary Fig. 3c and d).The radial strain field distribution along the microbubble's equatorial cross-section has a maximum negative value at φ = 0° (that is, the same direction of Fr), a maximum positive value at φ = 180° (that is, the opposite direction of Fr), and values of approximately zero at φ = 90° and 270° (that is, the direction perpendicular to Fr).The fiber taper amplifies the radial strain at the coupling position (that is, φ = 0° in the microbubble's equatorial cross-section), resulting in dR/R < 0 and a blueshift in the resonance wavelength.Then, an external force Fr was applied in the φ = 90° direction (Supplementary Fig. 4a), and the stress field distribution in the equatorial cross-section of mechano-sensor is shown in Supplementary Fig. 4b.The microbubble and fiber taper move in the φ = 90° direction, and the stress effect of the polymer matrix is also negligible in this case.The field distributions of the radial strain and strain-induced effective refractive index change along the equatorial cross-section of the microbubble are shown in Supplementary Fig. 4c and d, respectively.The radial strain field distribution is negative in the range of φ = 0° to 180° in S6 the equatorial cross-section but positive in the range of φ = 180° to 360°.When the radial strain field integral distributed within the equatorial cross-section of the microbubble are averaged, dR/R and dneff/neff are both approximately zero.This is because the radial strain at the coupling position (that is, φ = 0° in the microbubble's equatorial cross-section) is

Supplementary Note 4: Optimization of the Mechano-Sensor
To obtain a mechano-sensor with high displacement/force sensitivity, the geometric parameters of the micro-hair (that is, the glass capillary) and microbubble and the mechanical properties of the polymer matrix were optimized through the FEM scanning parameters.The outer contour of the microbubble can be approximately fitted with a Gaussian line shape:
where Rcapillary is the radius of the capillary, Rbubble is the radius of the microbubble, and α is related to the expansion length of the microbubbles along the z-axis and is only determined by the discharge area of the fiber fusion splicer.Supplementary Fig. 5a shows a microbubble with a radius of 160 μm and a wall thickness of 1.5 μm prepared from a fused silica capillary with a radius of 61.5 μm and a corroded thickness of 10 μm.The outer contour of this microbubble is fitted with a Gaussian line shape (red line): In conclusion, the curves equation for the inner and outer contours of the microbubble produced by the fiber fusion splicer (FSU-975) can be formulated as: where Tcapillary and Tbubble are the thicknesses of the capillary and microbubble walls, respectively.As shown in Supplementary Fig. 1, the strain effect on the microbubble is the main reason for the shift in the resonance wavelength, indicating that reducing Tbubble can effectively improve the displacement/force sensitivity of the mechano-sensor.In practice, considering that Tbubble is too thin to constrain the optical WGM and the stability of the preparation process, the thinnest Tbubble we can fabricate is 1.5 μm.Therefore, Tbubble is fixed at 1.5 μm in the following simulations and experiments.
Based on the principle of volume conservation during the preparation of the microbubbles and Equation (S4), once the geometric parameters of the capillary, including Rcapillary and Tcapillary, are determined, the radius of the prepared microbubble (Rbubble) can be obtained (Supplementary Fig. 5b).Rcapillary and Tcapillary are determined to optimize the displacement sensitivity of the mechano-sensor (SD).The FEM simulation results indicate that the larger the radius and wall thickness of the capillary are, the larger the radius of the prepared microbubble (Supplementary Fig. 5b), and ultimately, the higher the displacement sensitivity of the mechano-sensor (Fig. 2h).Because the circular symmetry of the prepared microbubble will be broken if Rbubble exceeds the limited discharge area of the fiber fusion splicer (FSU-975), Rbubble is limited to less than 190 μm (black solid line in Supplementary Fig. 5b and Fig. 2h).Finally, a fused silica capillary with a radius of 84 μm and a wall thickness of 8 μm is selected as the micro-hair (the star label in Supplementary Fig. 5b and Fig. 2h), and a microbubble with a radius of 185 μm and a wall thickness of 1.5 μm is fabricated for mechano-opto-transduction. In the FEM simulation, SD varies with the action point of the external force (L), as shown in Supplementary Fig. 5c.The outer contour curve of the prepared microbubble (Supplementary Fig. 5d) is fitted with a Gaussian line shape (red line): The final version of the bioinspired optical mechano-sensor is shown in Supplementary Fig. 6, which is composed of a thin-walled glass microbubble integrated with a glass micro-hair that is optically coupled with a fiber taper at the equator of the microbubble resonator.To fit the outer contour curve of the microbubble with a Gaussian line Here, ST and SD are the temperature and displacement sensitivities, respectively.The wavelength shifts of the two WGMs (Δλ1 and Δλ2) induced by temperature (ΔT) and displacement changes (ΔD) are defined as: Therefore, the changes in temperature and displacement can be solved by the following matrix: .
First, Supplementary Fig. 10a shows the evolution of the transmission spectra as the temperature increases from 27.7°C to 28.2°C at 0.1°C intervals, while the displacement is kept at 0 μm.The temperature sensitivities (ST1 and ST2) of the two tracked WGMs are -16.495pm °C-1 and -21.665 pm °C-1 , respectively (Supplementary Fig. 10b).The greater negative thermo-optical effect of the polymer matrix and the weaker positive thermo-optical effect of the glass wall both lead to the blueshift in the resonance wavelength with increasing temperature.
Because different WGMs have various energy ratios in the polymer matrix and glass wall, mode 1 and mode 2 have distinct temperature and displacement sensitivities.Mode 2 has more energy leakage than mode 1 in the polymer matrix, so mode 2 has a larger temperature sensitivity.However, mode 2 has a lower energy proportion in the glass wall with the largest strain effect, so the displacement sensitivity of mode 2 is smaller.
Finally, the evolution of the transmission spectra as the temperature and displacement changed concurrently was demonstrated (Supplementary Fig. 10e).By tracking the two above tracked WGMs and applying Equation S9, the displacement and temperature measurements can be decoupled, as shown in Supplementary Fig. 10f.The derived root mean square errors of the displacement and temperature are 20.15 μm and 0.027°C, respectively.
The results show that the mechano-sensor has good displacement-temperature decoupling stability.Moreover, compared to electrical mechano-sensors, the optical mechano-sensor has fascinating features, such as all-optical multifunctional perception system.
Moreover, to demonstrate that the mechano-sensor can work properly in saline and alkaline environments, the mechano-sensor was immersed in sea water.The sea water was prepared according to ASTM standard D1141-98 (2013, American Society for Testing Materials) 11 .An external force Fr (φ = 0°, L = 12 mm) is applied on the micro-hair, with the displacement increasing from 0 μm to 90 μm in steps of 30 μm (Supplementary Fig. 11a).
The calculated displacement sensitivity is -0.00255 pm μm -1 (Supplementary Fig. 11b).The result is comparable to that in Fig. 3e.Therefore, the force sensitivity is -3.131 pm mN -1 according to Fig. 3e, and the calculated external force Fr is shown in Supplementary Fig. 11c.
the entire WGM spectrum.Instead, the output wavelength remains at the rising or falling edge of the resonance dip, and the response time of the mechano-sensor can be accurately obtained by monitoring ∆I through the oscilloscope.The accurate response and recovery times of 1.24 ms and 1.26 ms, respectively, are obtained by applying a square waveform with a frequency of 0.2 Hz to the piezo actuator (Supplementary Fig. 13f).The mechano-sensor can detect a square waveform with a frequency up to 320 Hz, as demonstrated in Supplementary Fig. 13d and e.
Notably, while monitoring ∆I can accurately capture the response time of the mechano-sensor, this method is strongly dependent on the selection of the start position and the nonlinearity change in the intensity.Thus, it is more reasonable for us to investigate the perception capability of the mechano-sensor using the wavelength shift approach.MEMS barometers 16 Graphite pencil trace 17 CNT-Ag NP film 18,19 Graphene 20

Fig. 3 .
Simulations of the mechano-sensor under an external force Fr (φ = 0°).(a) Schematic illustration of the experimental device and FEM model of the mechanosensor under an external force Fr (φ = 0°).(b) Stress field distribution in the r-φ plane under an external force Fr (φ = 0°).(c) and (d) Field distributions of the radial strain and straininduced effective refractive index change along the equatorial cross-section of the microbubble under an external force Fr (φ = 0°), respectively.

Supplementary Fig. 4 .
approximately zero, resulting in a negligible strain amplification effect introduced by the fiber taper.There is no resonance wavelength shift when the external force Fr is applied in the φ = 90° or 270° directions.Simulations of the mechano-sensor under an external force Fr (φ = 90°).(a) Schematic illustration of the experimental device and FEM model of the mechanosensor under an external force Fr (φ = 90°).(b) Stress field distribution in the r-φ plane under an external force Fr (φ = 90°).(c) and (d) Field distributions of the radial strain and straininduced effective refractive index change along the equatorial cross-section of the microbubble under an external force Fr (φ = 90°), respectively.

5 .
58.54 μm is basically consistent with the capillary outer radius of 61.5 μm, and 160.14 μm is basically consistent with the microbubble outer radius of 160 μm.When the hollow fused silica capillaries are used to fabricate the hollow microbubbles, the volume of the glass remains constant, so the curve for the inner contour of the microbubble can be formulated as: Parametric scanning of the geometric parameters of the capillary and microbubble.(a) The outer contour of a microbubble is fitted with a Gaussian line shape (red line).Rbubble and Tbubble are 160 μm and 1.5 μm, respectively.Rcapillary and Tcapillary are 61.5 μm and 10 μm, respectively.(b) Relations between Rbubble and the geometric parameters of the capillary (i.e., Rcapillary and Tcapillary).Tbubble is fixed at 1.5 μm.The solid black line corresponds to the contour of Rbubble = 190 μm.The star label corresponds to the Rcapillary and Tcapillary selected for the micro-hair.(c) Simulations of the relations between the displacement sensitivity of the mechano-sensor (SD) and the position of the applied force (L) under an external force Fr (φ = 180°).(d) Outer contour of the microbubble fabricated for mechanoopto-transduction is fitted with a Gaussian line shape (red line).Rbubble and Tbubble are 185 μm and 1.5 μm, respectively.Rcapillary and Tcapillary are 84 μm and 8 μm, respectively.The scale bars in (a) and (d) represent 100 μm.
shape and quantitatively control the geometric parameters of the microbubble, the prepared microbubble is approximately 200 μm away from the melting node where the glass capillary is sealed.Notably, such a short distance of 200 μm does not affect the displacement sensitivity of the mechano-sensor.The radius (Rcapillary) and wall thickness (Tcapillary) of the glass capillary are 84 μm and 8 μm, respectively.The radius (Rbubble) and wall thickness (Tbubble) of the glass-based hollow microbubble are 185 μm and 1.5 μm, respectively.The 50 mm long micro-hair collects information about the mechanical stimuli in the environment, such as forces and vibrations, and propagates the information to the microbubble.The thinwalled microbubble configuration is mechanically flexible, allowing the device to transform these environmental mechanical stimuli into shifts in the WGM resonance wavelength and the spectral light signals (i.e., shifts in the dips).

Table 1 .
Comparison of the properties of commercial UV-crosslinked lowrefractive-index polymer.

Table 2 .
Comparison of the sensing performance of different types of force sensors.